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NF

Syntax

NF(F:POLY,I:IDEAL):POLY
NF(V:VECTOR,M:MODULE):VECTOR
    

Summary

normal form

Description

The first function returns the normal form of F with respect to I. It also computes a Groebner basis of I if that basis has not been computed previously.

The second function returns the normal form of V with respect to M. It also computes a Groebner basis of M if that basis has not been computed previously.

The coefficient ring is assumed to be a field. Note that the definition of normal form depends on the current value of the option FullRed of the panel GROEBNER. If FullRed is FALSE it means that a polynomial is in normal form when its leading term with respect to the the current term ordering cannot be reduced. If FullRed is TRUE it means that a polynomial is in NF if and only if each monomial cannot be reduced.

example

    
Use R ::= Q[x,y,z];
Set FullRed;
I := Ideal(z);
NF(x^2+xy+xz+y^2+yz+z^2,I);
x^2 + xy + y^2
-------------------------------
UnSet FullRed;
NF(x^2+xy+xz+y^2+yz+z^2,I);
x^2 + xy + y^2 + xz + yz + z^2
-------------------------------
        
    

See Also